If \(A\subseteq B\) and \(B\subseteq C\), which conclusion is always true?
Answer and explanation
Correct answer: \(A\subseteq C\)
Subset inclusion is transitive. Let \(x\) be any element of \(A\). From \(A\subseteq B\), we get \(x\in B\); from \(B\subseteq C\), we then get \(x\in C\). Hence every element of \(A\) belongs to \(C\), proving \(A\subseteq C\). The reverse inclusion, equality, or emptiness of B is not forced by the given information.
Frequently asked questions
What is the correct answer to this question?
\(A\subseteq C\)
Why is this the correct answer?
Subset inclusion is transitive. Let \(x\) be any element of \(A\). From \(A\subseteq B\), we get \(x\in B\); from \(B\subseteq C\), we then get \(x\in C\). Hence every element of \(A\) belongs to \(C\), proving \(A\subseteq C\). The reverse inclusion, equality, or emptiness of B is not forced by the given information.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
